Problem Statement

You are given $N$ integers $A_1,\ldots,A_N$ and a prime number $P$. Find the number of pairs of integers $(i,j)$ that satisfy both of the following conditions:

• $1 \leq i,j \leq N$;
• There is a positive integer $k$ such that $A_i^k \equiv A_j \mod P$.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i < P$
• $2 \leq P \leq 10^{13}$
• $P$ is prime.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N P
A_1 \ldots A_N

Output

Print the answer.